Heat Kernels and Dirac Operators: Vol 298 (Die Grundlehren der Mathematischen Wissenschaften) - Hardcover
Synopsis
The past few years have seen the emergence of new insights into the Atiyah-Singer Index Theorem for Dirac operators. In this book, elementary proofs of this theorem, and some of its more recent generalizations, are presented. The formula for the index of the Dirac operator is obtained from the classical formula for the heat kernel of the harmonic oscillator. The only prerequisite to reading this book is a familiarity with basic differential geometry. There are several chapters of preparatory material, including a treatment of connections and Quillen's theory of superconnections, characteristic classes, the theory of the heat equation and its solution on a compact manifold, Clifford algebras, Dirac operators and equivariant differential forms. The book finishes with a treatment of the index bundle and Bismut's local version of the Atiyah-Singer Index Theorem for families. As an application, the curvature of the determinant line bundle is calculated, following Bismut and Freed.
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Product Description
In this book, the Atiyah-Singer index theorem for Dirac operators on compact Riemannian manifolds and its more recent generalizations receive simple proofs. The main technique which is used is an explicit geometric construction of the heat kernels of a generalized Dirac operator. The first four chapters could be used at the text for a graduate course on the applications of linear elliptic operators in differential geometry and the only prerequisites are a familiarity with basic differential geometry. Several chapters deal with other preparatory material.
Review
Aus den Rezensionen:
"... Das vorliegende Buch ist die zweite korrigierte und erweiterte Ausgabe eines Werkes aus dem Jahre 1992. ... Ausgehend von einer Grundausbildung in klassischer Differentialgeometrie stellt das Buch alle zum Verständnis des Beweises notwendigen Voraussetzungen zur Verfügung. Dadurch eignet es sich einerseits zum Selbststudium für Studierende mit entsprechender Vorbildung ... andererseits als Grundlage einer Vorlesung über dieses ergiebige Thema."
(P. Grabner, in: IMN - Internationale Mathematische Nachrichten, 2006, Issue 202, S. 45)
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Heat Kernels and Dirac Operators
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Heat Kernels and Dirac Operators
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Trade paperback. Condition: New in new dust jacket. First edition. 1992. Corr. 2nd Printing. ***INTERNATIONAL EDITION*** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service. Sewn binding. Cloth over boards. 363 p. Grundlehren Der Mathematischen Wissenschaften (Springer Hardcover), 298. Audience: General/trade. Seller Inventory # K308A0000071
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Heat kernels and Dirac operators Nicole Berline, Ezra Getzler, Michèle Vergne. Grundlehren der mathematischen Wissenschaften 298.
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Berlin Heidelberg , Springer-Verl [1992]., 1992
ISBN 10: 3540533400
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Heat Kernels and Dirac Operators (Grundlehren der mathematischen Wissenschaften)
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